Nothing passes to the heirs of the deceased tenant. In some jurisdictions the magic words "with right of survivorship" must be used or the tenancy will assumed to be tenants in common. Tenants in common will have a heritable portion of the estate in proportion to their ownership interest which is presumed to be equal amongst tenants unless otherwise stated in the transfer deed. There are other types of estates in land that are used to prevent the alienation of land (also used in the law of trusts).
Generally these are called future interests, an example being the rule against perpetuities. See also the Rule in Shelley's Case.

